A bill to reform the House of Lords has been included in the Queen's speech as one of three constitutional bills, but severe doubts remain that the reforms will reach the statute book as David Cameron's aides continue to pour cold water over the plans.

Tory MPs are expected to mount a rebellion, with Labour support, over the debate timetable for the bill and the need for a post-legislative referendum.

The Liberal Democrats are for the moment relieved that the bill has made the programme.

Lord Strathclyde, the Conservative leader of the Lords, ostensibly supported the measure in a tongue-in-cheek interview in the Financial Times, but then stoked the rebellion by saying a reformed second chamber would be expensive, possess greater power and, if it had existed in the 1980s, would have blocked Thatcherite privatisation.

Ministers stressed on Wednesday that the reform can go through only if there is cross-party consensus.

The government has already published a draft bill, but the eventual bill will also reflect the government's response to a joint committee report on Lords reform.

The government on Wednesday set out areas of agreement between it and the joint committee: a mainly elected chamber, elected members voted on a system of single transferable vote, staggered elections with one third coming up for renewal at a time, peers to serve 15-year terms, current peers to leave in stages, a reduced number of peers, and powers to expel peers.

A briefing paper prepared by the Cabinet Office asserts that the bill would not change the powers and functions of the Lords, but many MPs believe that any newly elected second chamber would inevitably increase in authority, so setting up a clash with the Commons.

Ministers are concerned that any statute or memorandum setting out mutual powers will then make the relationship between Commons and Lords justiciable in English courts, so reducing the much prized autonomy of parliament.

The bill is to be introduced in the Commons and all its stages would have to be held on the floor of the house since it is a constitutional bill. More than 20 days would have to be set aside.

It is in the Commons that the bill's fate will be determined since Cameron has given a pledge to use the Parliament Act to force the bill through the Lords if it gets that far.

The Cabinet Office is also stewarding a bill to switch from household to individual registration, a measure promised by the outgoing Labour government.

The new register is due to be in place by 2014. The Cabinet Office gave no details of whether electoral registration officers would still be able to impose fines on individuals who refuse to co-operate. There is deep concern that even more poor people will fall off the register. The number of registered voters in turn determines the shape of parliamentary constituencies.

In addition, the Cabinet Office says work will continue to win Commonwealth agreement to reform the rules governing succession to the crown. These reforms will remove the right of men to have preference over women in succession to the crown, and also remove any discrimination against Catholics.